Abstract.A possibility measure can encode a family of probability measures. This fact is the basis for a transformation of a probability distribution into a possibility distribution that generalises the notion of best interval substitute to a probability distribution with prescribed confidence. This paper describes new properties of this transformation, by relating it with the well-known probability inequalities of Bienaymé-Chebychev and Camp-Meidel. The paper also provides a justification of symmetric triangular fuzzy numbers in the spirit of such inequalities. It shows that the cuts of such a triangular fuzzy number contains the "confidence intervals" of any symmetric probability distribution with the same mode and support. This result is also the basis of a fuzzy approach to the representation of uncertainty in measurement. It consists in representing measurements by a family of nested intervals with various confidence levels. From the operational point of view, the proposed representation is compatible with the recommendations of the ISO Guide for the expression of uncertainty in physical measurement.

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This paper deals with the problem of molten metal level control in continuous casting. Under normal circumstances, proportional integral derivative (PID) control performs quite well, but abnormal conditions (in particular nozzle clogging/unclogging) require manual intervention. Indeed, when the flow of matter into the mold increases suddenly, the PID controller is not always able to prevent large level variations that can even lead to mold overflow. So, a fuzzy controller has been designed using the expert knowledge of the operators for controlling the process during disturbed phases. The paper discusses both the design of the fuzzy logic controller and its integration with the PID in a global control architecture. Results from simulation and successful online implementation are presented.

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